Question

What is the wavelength of radiation with a frequency of `1.5 * 10^13` Hz? Does this radiation have a longer or shorter wavelength than red light?

Answer 1

The wavelength is `20 mum` which is longer than that of red light.

Explanation:

The only equation you need for this type of question is this one (which is the only one I remember!):

`c=nu*lambda`

where `c` is the speed of light, `nu` is the frequency and `lambda` is the wavelength. You can rearrange it anyway you need to. In this case:

`lambda=c/nu=(3.0*10^8m/s)/(1.5*10^13Hz)=2.0*10^-5m=20mum = 20000nm`

(Remember that `Hz` is `1/s`, so you can cancel that in the top and bottom leaving only `m`.)

Red light has a wavelength in the range of `620–750 nm`
(https://en.wikipedia.org/wiki/Visible_spectrum) which is much smaller than the `20000 nm` light above.

Note:

The equation above, `v = nu lambda`, works for any wave, where `v` is the speed of the wave and `nu` and `lambda` are frequency and wavelength respectively. The way I remember it is visual - the `nu` and the `lambda` have complementary shapes - they "fit together" when you look at them. You can also write `v=f lambda`, but that doesn't fit together so nicely.